Explain the minimum deviation angle for a prism using the graph of deviation angle versus incidence angle.

(N/A) The graph of experimentally measured values of the angle of deviation $\delta$ against the values of the angle of incidence $i$ is shown in the figure.
From the graph,it is clear that the value of the angle of deviation becomes minimum for only one particular value of the angle of incidence $i$.
Also,we can see that for two values of the angle of incidence,the angle of deviation is the same.
It has been experimentally established that for any given prism,the ray for which the angle of incidence $i$ and the angle of emergence $e$ are equal,the angle of deviation is minimum for that ray.
This angle is called the angle of minimum deviation $\delta_{m}$ of the given prism for the incident monochromatic light.
Note that,
when $i=e \Rightarrow \delta=\delta_{m}$
For a prism,
$i+e=A+\delta$
where $A$ is the prism angle.
Applying the condition for minimum deviation angle,
$i=e$ then $\delta=\delta_{m}$
$\therefore i+i=A+\delta_{m}$
$\therefore 2i=A+\delta_{m}$
$\therefore i=\frac{A+\delta_{m}}{2}$